Base field: \(\Q(\sqrt{-1}) \)
Generator \(i\), with minimal polynomial \(x^2 + 1\); class number \(1\).
Form
| Weight: | 2 | |
| Level: | 20808.3 = \( \left(42 i + 138\right) \) | |
| Level norm: | 20808 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no, but is a twist of the base change of a form over \(\mathbb{Q}\) | |
| Newspace: | 2.0.4.1-20808.3 (dimension 1) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) | |
| L-ratio: | 2 |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(i + 1\right) \) | \( -1 \) |
| \( 9 \) | 9.1 = \( \left(3\right) \) | \( 1 \) |
| \( 17 \) | 17.2 = \( \left(i - 4\right) \) | \( 1 \) |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 200 eigenvalues, of which 20 are currently shown below. We only show the eigenvalues $a_{\mathfrak{p}}$ for primes $\mathfrak{p}$ which do not divide the level.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 5 \) | 5.1 = \( \left(-i - 2\right) \) | \( 2 \) |
| \( 5 \) | 5.2 = \( \left(2 i + 1\right) \) | \( -2 \) |
| \( 13 \) | 13.1 = \( \left(-2 i + 3\right) \) | \( 2 \) |
| \( 13 \) | 13.2 = \( \left(2 i + 3\right) \) | \( 2 \) |
| \( 17 \) | 17.1 = \( \left(i + 4\right) \) | \( 2 \) |
| \( 29 \) | 29.1 = \( \left(-2 i + 5\right) \) | \( -6 \) |
| \( 29 \) | 29.2 = \( \left(2 i + 5\right) \) | \( 6 \) |
| \( 37 \) | 37.1 = \( \left(i + 6\right) \) | \( -6 \) |
| \( 37 \) | 37.2 = \( \left(i - 6\right) \) | \( 6 \) |
| \( 41 \) | 41.1 = \( \left(-4 i + 5\right) \) | \( 6 \) |
| \( 41 \) | 41.2 = \( \left(4 i + 5\right) \) | \( -6 \) |
| \( 49 \) | 49.1 = \( \left(7\right) \) | \( 14 \) |
| \( 53 \) | 53.1 = \( \left(-2 i + 7\right) \) | \( -2 \) |
| \( 53 \) | 53.2 = \( \left(2 i + 7\right) \) | \( -2 \) |
| \( 61 \) | 61.1 = \( \left(-6 i - 5\right) \) | \( 2 \) |
| \( 61 \) | 61.2 = \( \left(6 i - 5\right) \) | \( -2 \) |
| \( 73 \) | 73.1 = \( \left(-3 i - 8\right) \) | \( -10 \) |
| \( 73 \) | 73.2 = \( \left(3 i - 8\right) \) | \( 10 \) |
| \( 89 \) | 89.1 = \( \left(-5 i + 8\right) \) | \( 6 \) |
| \( 89 \) | 89.2 = \( \left(-5 i - 8\right) \) | \( 6 \) |